1. Field of the Invention
Broadly speaking, this invention relates to semiconducting, crystalline materials and methods of measuring their physical properties. More particularly, this invention relates to non-destructive, contactless methods and apparatus for accurately measuring the Hall coefficient and resistivity of semiconducting crystalline materials. The method and apparatus disclosed herein may be applied to piezoelectric semiconducting crystals particularly those in cubic class 43 m, which includes most of the II-VI and III-V compounds such as gallium arsenide.
2. Description of the Prior Art
There is presently great interest in accurately measuring the Hall coefficient and resistivity of high purity semiconductor materials such as gallium arsenide. This latter material is especially important because it exhibits a large band gap which renders it stable at high temperatures, while its large mobility permits high frequency devices to be made from the material.
Resistivity and Hall coefficient measurements at different temperatures play an important part in research on semiconductors, for it is from these quantities that the mobility and concentration of the charge carriers are found.
The Hall effect is discussed extensively in physics literature and is well known to those skilled in the semiconductor art. Briefly, if a magnetic field is applied in a direction normal to the direction of current flow in a conductor or semiconductor, a voltage is developed at right angles to both the direction of initial current flow and the direction of the magnetic field. In a semiconductor in which, for example, electrons dominate conduction, the Hall coefficient is given by: EQU R.sub.n =(1/en) (1)
where R.sub.n is in the electron Hall coefficient, e is the electronic charge, and n is the electronic concentration.
The conductivity is given by: EQU .sigma.=ne.mu..sub.n ( 2)
where n and e are defined above and .mu..sub.n is the electron mobility.
In a semiconductor in which both electrons and holes contribute substantially to the conduction process, the Hall coefficient is given by: EQU R=(R.sub.p .sigma..sub.p.sup.2 +R.sub.n .sigma..sub.n.sup.2)/(.sigma..sub.n +.sigma..sub.p).sup.2 ( 3)
where
R is the Hall coefficient, PA1 R.sub.p and R.sub.n are the hole and electron Hall coefficients respectively as defined above, PA1 .sigma..sub.p and .sigma..sub.n are the hole and electron conductivities as defined above.
Also the overall sample conductivity is given by: EQU .sigma.=.sigma..sub.n +.sigma..sub.p =ne.mu..sub.n +pe.mu..sub.p ( 4)
where .mu..sub.p is the hole mobility, p is the hole concentration, and other quantities have been defined above.
Those concerned with the measurements of Hall coefficients and resistivity have constantly sought methods and apparatus which will disturb the sample under test as little as possible. Present methods of measuring the Hall coefficient involve attaching a system of probes or electrodes to the surface of a specially cut sample. Apart from the problems of stray fields and very minute currents, the attachments which are made to the surface of the sample under test tend to interfere with measurement because the surface of the crystal is disturbed during the measurement process. A detailed discussion of the traditional methods of measuring the Hall coefficient is provided in the articles by L. J. Van der Pauw in Philips Research Reports, Vol. 13, 1958, pp. 1-9 and Philips Technical Review, Vol. 20,1958-1959, pp. 220-224.
The instant invention makes use of the fact that crystals in class 43 m are piezoelectric and can hence be made into acoustic resonators. As will be explained below, the contactless nature of the Hall coefficient measurement technique disclosed and claimed herein stems from the discovery that piezoelectric vibrators may be driven by an RF field in an air gap.
U.S. Pat. No. 4,353,027, entitled "Contactless Resistivity Measurement Method and Apparatus" issued to the present inventor and G. Iafrate, discloses a contactless measurement method and apparatus which yields resistivity data. The present invention provides both hall coefficient data and resistivity data without the need for contacting the sample.